In this third example, LVFPM was used to model the effects
of a vuggy porous oil-saturated dolomite on neutron and
density logs - i.e. finite pore size effects.  Bed thickness is not used.

The focus is on pore size effects at a fixed porosity.

In Figure 1, LVFPM heterogeneous bulk density decreases
linearly from 2.510 g/cc to 2.471 g/cc as pore size varies
from 0.0001 cm to 1.0 cm. The slope is –0.0386 g/cc per cm. From Figure 2, note that the corresponding heterogeneous density porosity increases from 0.117 pu to 0.140 pu at a rate of 0.0229 pu per cm over the same pore size interval.

In Figure 3 the heterogeneous neutron slowing down length increases from 9.954 cm to 11.464 cm as the pore size varies from 0.0001 cm to 1.0 cm.  This leads to the dramatic decrease in heterogeneous neutron porosity from 0.364 pu to 0.177 pu shown in Figure 3, as the LVFPM proxy model uses this slowing down length to compute neutron porosity.

Figure 4 shows that the heterogeneous neutron capture cross section (SIGMA) decreases linearly as the pore size increases; the slope is –0.0329 cu/cm.  Recall that SIGMA is interrelated with the thermal neutron diffusion length (L) and the thermal neutron diffusion coefficient (D) by the expression:

              D = (L**2)*SIGMA.

Figure 5 reveals the variation in heterogeneous thermal
neutron diffusion length and thermal neutron diffusion
coefficient as the pore size varies.  Although the change in
capture cross section (SIGMA) with pore size is not large
in this example, these variations of D and L with pore size
are an important aspect of the correction of SIGMA for
thermal neutron diffusion.

These variations with pore size also have important
implications for porosity logging based on the thermal
neutron diffusion coefficient [see U. S. Patent 3,818,225 and also the excellent review article “Nuclear Geophysics in Prospecting, Exploration and Development of Oil and Gas Fields” by E. V. Karus and Yu. S. Shimelevich, in All-Union Research Institute of Geophysics, 8 Warshavskoye Shosse, M-105, Moscow, USSR; also published in 1983: International Journal of Applied Radiation and Isotopes, v. 34, no. 1, p. 95-117, by Elsevier Science Ltd.]